Is there any classifier that works best in general for NLP based projects?
The accuracy depends on various factors. Might not always be the algorithm. For example a cleaner data with a poor algorithm might still give better results and vice versa. 

What are the preprocessing techniques you are using? This preprocessing techniques article is a good starting point for html data. And by vectorising I assume you mean word2vec, use a pre-trained word2vec model. Like google's word2vec model it's trained on a lot of data(about 100 billion words). 

LSTM performs good whenever the intent of the sentence is important. Check out this.
Ram hit Vijay and Vijay hit Ram, might mean the same to most algorithms. Example, Naive Bayes.